This work is based on modification of the general relativity, which includes effects of production /absorption of matter by the vacuum. The theory (without fitting parameters) is in good quantitative agreement with cosmological observations (SnIa, SDSS-BAO and reduction of acceleration of the expanding universe). In this theory we get rid of major controversies (Big Bang, critical density of the universe, dark energy, inflation). Based on exact Gaussian solution for the scale factor, it is shown that an effective age of the universe is about 327 billion years. Production of dark matter particles have started 43 billion years later. Supplementary exact solutions for the scale factor are obtained for various ranges of parameters. As an important bonus in this theory, we got interface between dark and ordinary matter, which very likely exist not only in cosmos, but everywhere, including our body and, especially, our brain. Subjective experiences are considered as a manifestation of that interface. This opens a possibility of a "communication" with dark matter. Probable applications of these ideas include health, communication, computational power and energy resources.